Falling plates, like bowling pins, can be deceptive if you have not practiced shooting them beforehand. The fact that they react to your shot often tends to make you want to look up (away from your sights) and watch them fall.
This is a bad idea, because you will miss your next shot, and perhaps your next several shots because you are now looking AT the plates instead of seeing them through your sights. Watch your sights. Try to stick with a load that recoils as little as possible.
I agree with growr that a heavy revolver using .38 Specials is just about the ideal plate gun. The best ever plate score I did in a match was 47/48 using a lightly loaded 1911 in .45 with iron sights that hardly recoiled at all...but my NORMAL plate average is around 42 - 46 plates and on everything but exceptional days I find it easier to do that with revolvers.
I suppose someday I should try to shoot the plates with a "dot" sight and see what happens...but I am just too dedicated to the iron sight method to make the investment, you know?
Watch your sights, not the plates. If you start missing, make that little voice in your mind yell "get back on the sights!". If the rules allow you to go prone (as they should) at 25, consider doing it and practice that a bit. Getting 4, 5 or 6 out of 6 at 25 yards can really help the score and it's better than the 2, 3 or 4 you are liable get if you stay on your feet. Just my two cents worth.